If w + x is < 0, is w - y > 0?

[gmatdriller]

After several failed searches for the question, I have decided to post it.

Don't know why [spoiler](1) /spoiler] is wrong.

If w + x is < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w

seems correct to solve this way:
combining stem (w+x < 0) with (1) - x+y<0, we have the 2 inequalities:

w + x < 0............(i)
x + y < 0.............(ii)
............................ SUBTRACTING (i) from (ii)
w - y < 0 If w<y, definitely w CANNOT be greater than y
(question asked) at the same time...SUFFICIENT
Correct response is NO "w is NOT > y" as asked.

(ii) I have no issues with that.

[Rahul@gurome]

After several failed searches for the question, I have decided to post it.

Don't know why [spoiler](1) /spoiler] is wrong.

If w + x is < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w

seems correct to solve this way:
combining stem (w+x < 0) with (1) - x+y<0, we have the 2 inequalities:

w + x < 0............(i)
x + y < 0.............(ii)
............................ SUBTRACTING (i) from (ii)
w - y < 0 If w<y, definitely w CANNOT be greater than y
(question asked) at the same time...SUFFICIENT
Correct response is NO "w is NOT > y" as asked.

(ii) I have no issues with that.

You cannot subtract inequalities like this. It's not equation! Only thing we know from question stem and statement 1 is both (w + x) and (x + y) is less than zero. We don't which one of them is greater than the other. When you're subtracting (x + y) from (w + x) it could be positive or negative. For example say, (w + x) = -4 and (x + y) = -7 => (w + x) - (x + y) = 3 > 0.

But we can add them and say (w + 2x + y) < 0, because there is no way addition of two negative number will result in a positive number.

Hope it helps.

[ankurmit]

What is OA of this quistion ?

[gmatdriller]

Rahul, i got it now.
While the differecnce between two negatives can be either positive or
negative, their sum is always negative.


Thanks.
Source: GMATPrep
OA is B.

[junegmat221]

@Rahul,
Can u please detail us on what are the strict guidelines to be followed ,
When dealing with inequalities like the one above.

You cannot subtract inequalities like this. It's not equation! Only thing we know from question stem and statement 1 is both (w + x) and (x + y) is less than zero. We don't which one of them is greater than the other. When you're subtracting (x + y) from (w + x) it could be positive or negative. For example say, (w + x) = -4 and (x + y) = -7 => (w + x) - (x + y) = 3 > 0.

It would be of much help..
Thanks..

[Rahul@gurome]

@Rahul,
Can u please detail us on what are the strict guidelines to be followed ,
When dealing with inequalities like the one above.

It would be of much help..
Thanks..

Always cases:

• Positive + Positive = Always positive
  Positive - Negative = Always positive
  Negative - Positive = Always negative
  Negative + Negative = Always negative

We can add or subtract accordingly without any problem or error.

May be cases:

• Any combination other than those above are may be positive or negative.

We cannot add or subtract them to get a sure result unless there are other conditions involved.